Subgroups — #26013687

Order 11168.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19150234	C₂	1	4	yes	maximal, complemented
2	#19150233	C₂	1	6	yes	maximal, complemented
3	Q₈×D₃₄₉	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₆₉₈	C₂²	1	6	yes	—
6	D₁₃₉₆	C₂²	1	6	yes	—
7	C₂²⋊D₃₄₉	C₂²	1	4	yes	—
8	C₄×D₃₄₉	C₂²	1	12	yes	—
9	Q₈×C₃₄₉	C₂²	1	4	yes	—
10	C₂×C₄×C₃₄₉	C₂²	1	3	yes	—
11	C₂²×C₃₄₉	C₂³	1	1	yes	characteristic
12	C₂×D₃₄₉	C₂³	1	4	yes	—
13	C₄×C₃₄₉	C₂³	1	6	yes	—
14	Dic₃₄₉	C₂³	1	4	yes	—
15	C₂×C₃₄₉	—	2	1	no	—
16	C₂×C₃₄₉	C₂⁴	1	1	yes	characteristic
17	D₃₄₉	—	2	4	no	—
18	C₃₄₉	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
19	2₋¹⁺⁴	—	349	1	no	maximal, Sylow
20	#41	—	349	4	no	—
21	#41	—	349	6	no	—
22	C₂×Q₈	—	349	4	no	—
23	C₂×Q₈	D₃₄₉	1	1	yes	characteristic, complemented
24	Q₈	—	349	6	no	—
25	Q₈	C₂×D₃₄₉	1	4	yes	—
26	D₄	—	349	4	no	—
27	D₄	—	349	6	no	—
28	C₂×C₄	—	349	12	no	—
29	C₂×C₄	C₂×D₃₄₉	1	3	yes	—
30	C₂²	—	349	4	no	—
31	C₂²	C₂²×D₃₄₉	1	1	yes	characteristic
32	C₄	—	349	4	no	—
33	C₄	C₂²×D₃₄₉	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	698	4	no	—
36	C₂	C₂³×D₃₄₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.